On the connectivity of unit distance graphs (Q1923783)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the connectivity of unit distance graphs |
scientific article; zbMATH DE number 934041
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the connectivity of unit distance graphs |
scientific article; zbMATH DE number 934041 |
Statements
On the connectivity of unit distance graphs (English)
0 references
6 March 1997
0 references
Given a field \(K\subseteq R\) and an integer \(d>1\), the graph \(G(K^d)\) is defined whose vertices are elements of \(K^d\), with an edge between any two points at (Euclidean) distance 1. The author proves that \(G(K^2)\) is not connected while \(G(K^d)\) is connected for \(d\geq5\); \(G(K^4)\) is connected if and only if \(G(K^3)\) is connected. Also necessary and sufficient conditions for the connectedness of \(G(K^3)\) are given.
0 references
unit distance graphs
0 references
connectedness
0 references
